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Non-deterministic imperfect information games pose challenges for Artificial Intelligence (AI) design, as compared to AI for perfect information games. Monte Carlo Tree Search (MCTS), an AI technique that uses random sampling of game playouts to build a search tree rather than domain-specific knowledge about how to play a given game, has been used successfully in some perfect information games. MCTS has also been implemented for imperfect information board and card games, using techniques including sampling over many determinizations of a starting game state, and considering which information set each player belongs to. In this paper, we first describe the imperfect information card game Cribbage and the MCTS algorithm. We then describe our implementation of Cribbage for two players and several MCTS and non-MCTS-based AI players. We compare their performance and find that Single-Observer Information Set MCTS performs well in this domain.